 ;;; validation methods
 
 (defn dependent?
-  "Checks if a dependency is valid. Scales must be given as map between 
-   attributes and contexts."
+  "Checks if a dependency between attributes is valid. Attributes depend
+   on another set of attributes if they can be expressed by them, i.e. 
+   given a context (G,M,I), the set Y depends on the set X of attributes
+   if every extent of the concepts of (G,M,I_{X u Y}) is an extent of
+   a concet of (G,M,I_{X}).
+   Scales must be given as map between attributes and contexts."
   [mv-ctx scales impl]
   (let [default (fn [a] (make-context-nc #{} #{} #{}))
         ctx-pc  (scale-mv-context 

       (extents ctx-pc))))

(defn weakly-dependent?
  "Checks if a weak dependency is valid. Scales must be given as map
   between attributes and contexts."
  [mv-ctx scales impl]
  (let [default (fn [a] (make-context-nc #{} #{} #{}))
        ctx-p  (scale-mv-context 

             (set (extents ctx-c)))))

(defn functional-dependent?
  "Checks if a functional dependency is valid. A set Y is functinally dependet
   on a set X of a mv-context if for some objects g and h
   x(g) = x(h) for all x in X implies y(g) = y(h) for all y in Y."
  [mv-ctx impl]
  (let [inz   (incidence mv-ctx)
        objs  (objects mv-ctx)
